This article introduces edge-forming schemes for image zooming of color images by general magnification factors. In order to remove/reduce artifacts arising in image interpolation such as image blur and the checkerboard effect, an edge-forming method is suggested to be applied as a post-process of standard interpolation methods. The method is based on non-convex nonlinear partial differential e...

This paper proposes a novel hybrid FDTD method for solving the time-dependent Schrödinger equation, which is fundamental modeling materials and designing nanoscale devices. The wave function propagated on nonuniform grids by applying explicit updates in part of grid implicit elsewhere. latter are based Alternating-Direction Implicit (ADI) scheme while former constructed with central difference ...

tions (PDEs). This class of schemes is based on three principal observations. First, the spatial discretization of parabolic PDEs results in stiff systems of ordinary differential equations (ODEs) in time, and therefore, requires an implicit method for its solution. Spectral Deferred Correction (SDC) methods use repeated iterations of a low-order method (e.g. implicit Euler method) to generate ...

Bipolar semiconductor device 2D FDTD modelling suited to parallel computing is investigated in this paper. The performance of a second order explicit approximation, namely the Nessyahu-Tadmor scheme (NT2) associated with the decomposition domain method, are compared to a classical quasi-linear implicit one based on the Alternating Direction Implicit method (ADI). The comparison is performed bot...

A nonlinear Poisson equation (NPE) has been introduced to model and nonlocal hyperpolarisation effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due a strong nonlinearity associated with the heterogeneous dielectric media, NPE is difficult solve numerically large protein systems. new pseudo-transient continuation approach proposed this paper efficiently st...

The (Extrapolated) Alternating Direction Implicit Preconditioners for the class of Conjugate Gradient Methods are applied for the solution of the second order elliptic equation in a rectangle under Dirichlet boundary conditions. The PDE is approximated by uniform meshes of 5− and 9−point difference schemes and analytic expressions for the optimal acceleration and extrapolation parameters are ob...

Diierential cryptanalysis is a powerful attack developed by Eli Biham and Adi Shamir. It has been successfully applied to many DES-like cryptosystems. We provide a brief introduction to their paper BS91] and show how to apply diierential cryptanalysis to attack the Data Encryption Standard (DES) reduced to 5 rounds.

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an alternative direction implicit (ADI) splitting method for its numerical solution. To treat the high-order and mixed derivative terms in the equation we adopt an ADI method by Hundsdorfer and Verwer to the present setting. The paper is furnished with numerical results for the evolut...

We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals—an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors “waver” over time in the relative weight they put on them. The model predicts that good news about fundamentals can trigger large...